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Economic production function

- 1. Unit - IV
- 2. Introduction Whatever be the objective of business firms, achieving optimum efficiency in production or minimizing the cost of production is one of the prime concerns of managers today. Infact, the survival of the firms in a competitive market depend on their ability to produce at a competitive cost.
- 3. Production Refers to the transformation of resources into outputs of goods and services. General motors hires workers who use machinery in factories to transform steel, plastic, glass, rubber and so on into automobiles.
- 5. Production Function States the relationship between inputs and outputs Inputs – the factors of production classified as: Land – all natural resources of the earth. Price paid to acquire land = Rent Labour – all physical and mental human effort involved in production Price paid to labour = Wages Capital – Money, buildings, machinery and equipment used for the production. Price paid for capital = Interest
- 6. Production Function Inputs Process Output Land Labour Capital Product or service generated – value added
- 7. Fixed and Variable Inputs Variable Input : one whose quantity may be varied in the short run and the long run. Fixed Input : one whose quantity may not be varied in the short run, but may be varied in the long run.
- 8. Analysis of Production Function: Short Run In the short run at least one factor supply is variable but all other factors can be changed. Reflects ways in which firms respond to changes in output (demand). Can increase or decrease output using more or less of some factors but some likely to be easier to change than others Increase in total capacity only possible in the long run
- 9. Analysing the Production Function: Long Run The long run is defined as the period of time taken to vary all factors of production By doing this, the firm is able to increase its total capacity – not just short term capacity Associated with a change in the scale of production The period of time varies according to the firm and the industry. In electricity supply, the time taken to build new capacity could be many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months!
- 10. Production Function Production function is defined as “the functional relationship between physical inputs ( i.e., factors of production ) and physical outputs, i.e., the quantity of goods produced”. Production function may be expressed as under: Q = f ( K,L) Where ; Q = Output of commodity per unit of time. K = Capital. L = Labour. f = Functional Relationship.
- 11. Production function depends on : Quantities of recourses used. State of technical knowledge. Possible process. Size of firms. Relative prices of factors of production. Combination of factors.
- 12. The following points may be emphasized: Production function represents a purely technical relationship. Output is the result of joint use of factors of production. Combination of factors depend on the state of technical knowledge. Every management has to make choice of the production function which gives average cost and maximum average profit.
- 13. Laws of Production Laws of production are of two types: The law of variable proportions. Laws of returns to scale.
- 14. The Law of Variable Proportions Is the answer to the question: How will total output change when all inputs are fixed except one input. Two ways to illustrate the answer: Production schedule (chart) Production function (graph) Usually, as in this example, labor is the variable input; all other are held constant.
- 15. Short Run Production Function: The Law of Variable Proportions Statement of the law: “The law of variable proportions states that when more and more units of the variable factor are added to a given quantity of fixed factors, the total product may initially increase at an increasing rate reach the maximum and then decline”.
- 16. Tabular Presentation of Law of Variable Proportions Units of Labour TP MP AP I Stage II Stage III Stage 1 80 80 80 2 170 90 85 3 270 100 90 4 368 98 92 5 430 62 86 6 480 50 80 7 505 24 72 8 505 0 63 9 495 -9 55 10 470 -25 47
- 17. Diagrammatical Presentation of Law of Variable Proportions Assumptions of the law: State of Technology remains the same. Input prices remain unchanged, Variable factors are homogeneous. AP MP AP MP
- 18. Conclusions While adding units of an input (labor), the marginal product goes through three stages: Stage I (Increasing returns): marginal product increases throughout. This means that every additional unit increases productivity as well as total output. This is shown on the graph by an increasing slope.
- 19. Conclusions, cont. Stage II (diminishing returns): marginal product decreases throughout. This means that every additional unit decreases productivity, though total output still increases. This is shown on the graph by a decreasing positive slope.
- 20. Conclusions, cont. Stage III (negative returns): marginal product is negative throughout. This means that each additional unit actually decreases total output. a waste of money and resources. This is shown on the graph by a negative slope.
- 21. Conclusions, cont. The greatest productivity is at the end of Stage I. The greatest output is at the end of Stage II. Therefore, Stage II is ideal, because there is a balance between productivity and total output.
- 22. Law of Diminishing Returns and Business Decisions A Rational producer will never choose to produce in stage III where Marginal Productivity of variable factor is negative. It will stop at the end of the second stage where Marginal Productivity of the variable factor is Zero. At this point the producer is maximizing the total output and will thus be making the maximum use of the available variable factors. A producer will also not choose to produce in Stage I where he will not be making full use of the available resources as the average product of the variable factor continues to increase in this stage. A producer will like to produce in the second stage. At this stage Marginal and Average Product of the variable factor falls but the Total Product of the variable factor is maximum at the end of this stage. Thus stage II represents the stage of rational producer decision.
- 23. Key Concept: Marginal Product Marginal product is the amount that total output increases by adding one more unit of an input. Marginal product is calculated by subtracting the most recent total product (# of units produced) from the new total product.
- 24. Law of Return to Scale The word scale refers to the long-run situation where all inputs are changed in the same proportion. The results might be constant, increasing or decreasing returns.
- 25. Constant Return to Scale Refers to the situation where output changes by the same proportion as inputs Eg if all inputs are increased by 10%, output also rises by 10%, Inputs are doubled then output is also doubled
- 26. Increasing Return to Scale Refers to the case where output changes by a larger proportion than inputs Eg if all inputs are increased by 10%, output rises by more than 10%, Inputs are doubled then output is more than doubled Division of labour & Specialisation
- 27. Decreasing Returns to Scale Refers to the case where output changes by a smaller proportion than inputs Eg if all inputs are increased by 10%, output rises by less than 10%, Inputs are doubled then output is less than doubled Managerial Diseconomies
- 28. In their effort to minimize the cost of production, the fundamental questions which managers are faced with, are:- How are the Production and Costs related ? Does substitution between the factors affects the Cost of Production? How does the technology i.e., factor combination matters in reducing the cost of production ? How can the least cost combination of inputs be achieved ? What happens to rate of return when more plants are added to the firm ? What are the factors which create economies and diseconomies for the firm ? The theory of production provide answers to these questions by providing tools and techniques to analyze the production conditions and to provide solution to the practical business problems.
- 29. Long Run Production Function: The Returns to scale The long run production function is termed as returns to scale. In the long run, the output can be increased by increasing all the factors in the same proportions. The laws of returns to scale is explained by the help of Isoquant curves. An Isoquant curve is the locus of points representing various combination of two inputs, Capital & Labour, yielding the same output. There are three technical possibilities; a) Total output may increase more than proportionately: Increasing returns to scale, b) Total output may increase at a constant rate: Constant Returns to Scale, c) Total output may increase less than proportionately: Diminishing returns to scale.
- 30. Three Stages of Law of Diminishing Returns Increasing Returns Increasing Returns Constant Returns Diminishing Returns Scale of Inputs Marginal Product
- 31. Isoquant is one way of presenting the production function where two factors of production are shown. It represents all possible input combinations of the two factors, which are capable of producing the same level of output. IQ O Y X a b c d LABOUR C A P I T A L ΔK ΔL ΔK ΔL ΔK ΔL
- 32. Marginal rate of technical substitution indicates the rate at which factors can be substituted at margin in such a way that the total output remains unaltered. MRTS of L for K is defined as the quantity of K which can be given up in exchange for an additional unit of L, so that level of output remains the same. The MRTS at a point on the isoquant can be measured by the slope of isoquant at that point. Slope of IQ at point b = ΔK/ΔL. MRTS = Slope = ΔK/ΔL. MRTS can be known from the ratio of MPP of two factors. As output remains the same at every point of isoquants so loss in physical output from a small reduction in K will be equal to the gain in physical output from a small increment in L.
- 33. Marginal rate of technical substitution indicates the rate at which factors can be substituted at margin in such a way that the total output remains unaltered. MRTS of L for K is defined as the quantity of K which can be given up in exchange for an additional unit of L, so that level of output remains the same. The MRTS at a point on the isoquant can be measured by the slope of isoquant at that point. Slope of IQ at point b = ΔK/ΔL. MRTS = Slope = ΔK/ΔL. MRTS can be known from the ratio of MPP of two factors. As output remains the same at every point of isoquants so loss in physical output from a small reduction in K will be equal to the gain in physical output from a small increment in L.
- 34. Thus, Loss of output = Gain of output i.e. [(Reduction in K ) X (MPP of K)] = [(Increment in L) X (MPP of L)] OR, ΔK X MPK = ΔL X MPL ΔK = MPL ΔL MPK OR, MRTSLK = MPL ( By definition ΔK = MRTS LK = Slope of isoquant at that point )MPK ΔL Thus, MRTSLK is the ratio of marginal physical productivities of the two factors.
- 35. Combinations Labour (L) Capital (K) MRTS L K A B C D E 1 2 3 4 5 12 8 5 3 2 - 4:1 3:1 2:1 1:1 Tabular Presentation of MRTSLK
- 36. Iso-Cost Lines It shows all the combinations of the two factors ( say labour and Capital) that the firm can buy with a given set of prices of two factors. It plays an important role to determine combinations of factors, the firms will choose for production ultimately to minimize cost. O X Y PRICE OF LABOUR P R I C E OF C A P I T A L A B C D E E F
- 37. Producers Equilibrium or the Least Cost Combination of Factors A producer desires to minimise his cost of production for producing a given level of output with the least cost combination of factors. E P R S T IQ IQ1 IQ2 LABOUR C A P I T A L A B O X Y How producers ultimately arrives the point of equilibrium ? •The equilibrium is achieved at the point Where MRTS LK = PL/PK ie • The slope of isoquant =Slope of isocost •Or , MRTS LY = MPL = PX MPK PY Or, MPL = MPK PX PY
- 38. Expansion Path The Line joining the least cost combinations like a, b, c, d. Expansion Path may be defined as the locus of efficient combinations of the factors. Expansion Path y o x a b c IC IC1 IC2 LABOUR C A P I T A L A B C D E F
- 39. a) Increasing Returns to Scale: Causes: Indivisibilities of Factors, High degree of specialization, Labour C A P I T A L
- 40. b) Constant Returns to Scale Causes: Factors of production fully utilised. Technology remains unchanged C A P I T A L
- 41. c) Diminishing Returns to Scale Causes: Managerial Diseconomies. Scarce and Exhaustible resources. Labour C A P I T A L
- 42. Economies & Diseconomies of Scale The Factors which cause the operations of the Laws of Returns to Scale are grouped as under; Economies of Scale, relates to profit accruing to a business firm. Economies of scale are classified as; Internal economies External economies,
- 43. Internal Economies Economies in production • Technical advantages, • Advantages of division of Labour and specialization Economies in Marketing Managerial Economies Economies in Transportation & storage
- 44. External Economies to large size firms arise from the discounts available to it due to; Large scale of purchase of raw material, Finance at low rate of interest, Low advertising cost, Low Transportation cost. Diseconomies of scale are the losses accruing to a business firm as a result of large scale production.